1. Field of the Invention:
The invention relates to methods and apparatus for determining the altitude of a signal propagation path.
2. Description of the Prior Art:
Cognizance of the effects of the atmospheric refractive index gradient is essential to an accurate determination of the altitude of electromagnetic or radio signals propagated through the lower atmosphere. Normally, the refractive index gradient causes a downward curvature of horizontally launched electromagnetic signals which is about one-fourth that of the earth. However, under unusual meteorological conditions, the radio energy may be confined to thin layers near the earth's surface with resultant abnormally high field strength being observed beyond the normal radio horizon. At other times a transition layer between differing air masses will give rise to the reflection of radio energy. In addition to these gross profile effects, the atmosphere is always more or less turbulent, with the result that radio energy is scattered out of the normal antenna pattern. In addition to the vertical structure of the atmospheric index, there are variations associated with changing latitude and longitude as well as temporal (diurnal and seasonal) variations which are directly related to the energy balance of the earth. No standard compensation for radio wave curvature, can provide acceptable accuracy under the wide range of temperature and humidity conditions encountered.
In the prior art, signal range and antenna elevation angle have been employed in three basic methods for determining the altitude of a transmitted radar pulse. The first method assumes that the earth is flat and determines altitude by multiplying the pulse range (R) by the sine of the elevation angle (.theta.). This "flat earth" method may be mathematically expressed as: EQU H = R sin .theta. (1)
The second method assumes that the earth is a sphere of radius R.sub.e, having no atmosphere. Altitude is determined from an approximation obtained by expanding the exact solution of a quadratic equation developed from the geometry of a spherical earth and a straight line path of the radar pulse. This "spherical earth -- no atmosphere" method may be mathematically expressed as: EQU H = R sin .theta. + R.sup.2 /(2R.sub.e) (2)
The second term in the right side of equation (2) is, in effect, a correction for the assumption of a flat earth made in the first method. The third method assumes a spherical earth with a particular type of atmosphere. This method attempts to account for the curvature or bending in the signal propagation path which is due to spatial variations in the atmospheric index of refraction. A constant refractive index curvature is simply added to the curvature of the earth. The radius of the resulting curve is an effective earth's radius, R.sub.ef which is a factor (K) times the actual earth's radius, R.sub.e, used to determine altitude in the second method. This "effective earth radius" method can be mathematically expressed as: EQU H = R sin .theta. + R.sup.2 /(2R.sub.ef) (3)
where
R.sub.ef = KR.sub.e
Since a typical value for the constant K for an average atmosphere over the continential United States is (4/3), this method is also known as the "4/3 -- earth's radius method".
The "flat earth" and "spherical earth-no atmosphere" methods ignore the effects of the atmospheric refractive index gradient and therefore inaccurately determine the altitude of electromagnetic signals propagated through the atmosphere. Most prior art signal processes which have attempted to account for the effects of the atmospheric refractive index gradient have determined altitude based on the "effective earth's radius" method assuming that the curvature of the propagation path is constant regardless of the altitude of the propagation path or the initial elevation angle of the transmitted signal. Since the propagation path depends on non-linear, dynamic spatial variations in the index of refraction of the propagation atmosphere, the accuracy of this prior art method has also been limited.
Some prior art data processors have utilized a realistic atmospheric model to determine signal propagation curvature caused by the refractive index gradient but this has not been done on a real-time basis. These data processors have determined altitude as a function of range, with the transmitting antenna elevation angle and range as input data so that a continuous, real-time altitude determination is impossible. Under these circumstances, altitude can be determined only by an iterative search for the altitude which is appropriate for the input range. Such iterative methods make these prior data processors highly unsuitable for high speed applications. In addition, these prior art data processors fail to compute accurately if the signal propagation path approaches a line tangent to the earth's surface because one of the calculated parameters approaches infinity. In practice, however, the signal propagation path can become tangential to the earth's surface under typical atmospheric conditions when the signal is launched at a negative angle, or when atmospheric conditions cause sufficient curvature to overcome an initial positive transmission angle.